Statistics Canada’s Survey Methodology for the New Services Producer Price Index Surveys
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Statistics Canada’s Survey Methodology for the New Services Producer Price Index Surveys
By: Saad Rais, Statistics CanadaZdenek Patak, Statistics
Canada
Statistique StatisticsCanada Canada
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Outline of Presentation
Introduction Sampling Design Estimation Outlier Detection Conclusion
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Introduction
What is a Price Index? Proportionate change in the price of
goods or services over time
What is its purpose? Deflator Indicator
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Introduction
Users: Government departments Private companies Economists, analysts, researchers etc.
Examples: Consumer Price Index Import and Export Price Index Producer Price Index
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Introduction
Price Indices in Canada Price indices were mostly limited to the
goods sector 2003 - Service industry accounted for
75% of employment and 68% of the GDP in Canada
Five year plan to produce a set of Services Producer Price Indices (SPPI)
Focus on a survey methodology that is based on sound statistical principles
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Sampling Design
Two Stage Design: Sampling of businesses Sampling of items within each business
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Sampling Scheme
Common method: Judgmental sampling Straightforward sampling and
estimation Absence of a complete reliable frame Limited resources Statistical quality measures cannot be
calculated
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Sampling Scheme
Cut-off sampling Yields a sample with the optimal
coverage of some size measure variable – revenue in our surveys
Susceptible to biased estimates No sample rotation
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Sampling Scheme
Stratified Simple Random Sampling Without Replacement (Stratified SRSWOR) Common Sampling scheme for business
surveys A probability sample Abundance of literature Size stratification Each unit has equal probability of
selection
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Sampling Scheme
Probability Proportional-to-Size (PPS) Sampling Probability sampling High revenue coverage in sample Requires appropriate size measure Not robust to errors in measure of size
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Sampling Scheme
Sequential Poisson Sampling All the desirable properties of Poisson
Sampling Additional benefit: fixed sample size
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Sampling Design
First-Stage Frame Statistics Canada’s Business Register
Primary Sampling Unit Varied from survey to survey, ranging from
establishment, company, enterprise
Primary Stratification By industry line Sometimes by province
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Sampling Design
Stratum Allocation x – optimal allocation, where x = unit
revenue (Särndal, et al., (1992)) Adjustment for over-allocation
(Cochran (1977)) Adjustment for under-allocation
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Sampling Design
Sample Size Based on availability of resources and
expert knowledge and experience No previous or related data available
to anticipate response rate or target a CV to estimate a sample size
Improvements to sample size will be made after obtaining sufficient data
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Sampling Design
Size Stratification TN units: the smallest revenue-
generating units that contribute to 5% of the applicable primary stratum.
TA units: Any units for which TS units: Units for which
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Sampling DesignSecond Stage Sampling: Selection of
Items PPS sampling scheme
Requires a list of items for each business unit
Resource intensive, high response burden
Therefore a judgmental sample is selected Concerns:
No variance estimation Sampling bias could result from not
pricing representative items
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Estimation
Estimation in 2 stages: Elemental Indices Aggregate Indices
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Estimation
Elemental Index: Jevons Index
Exhibits desirable economic and axiomatic properties
Closer to Fisher’s index Cannot use zero or negative prices
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Estimation
Target Aggregate Index: Laspeyres Index
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Ratio Estimator:
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Estimation
Cancellation of economic weights and sampling weights:
However, in the presence of non-responding units, cancellation of weights does not occur.
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Estimation
Variance Estimation:Approximated using the Taylor linearization
method:
In Poisson sampling, since when , the formula reduces to:
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Outlier Detection
α-trimming Proportion α is removed from tails Requires prior knowledge to be efficient
Interquartile range Handles up to 25% aberrant observations Construct robust z-score to identify outliers
MAD (Median Absolute Deviation) Handles up to 50% aberrant observations Construct robust z-score to identify outliers
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Conclusion
Current and future projects Research on the efficiency of PPS
sampling versus SRSWOR sampling Outlier detection methods Imputation methods Bootstrap variance estimation
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Conclusion Services industry is an integral
component of our economy We are currently in the
pilot/developmental stage of index production
With the collection of data, efficiencies in the sample size, and further research will help improve our methodology
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Thank YouPour de plus amples informations ou pour obtenir une copie en français du document veuillez contacter:
For more information, or to obtain a French copy of thepresentation, please contact:
Statistique StatisticsCanada Canada
Saad RaisE-Mail: saad.rais@statcan.ca
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